Question

Ratio of the roots of the quadratic equation x^2 – 11x + 30 = 0 is
(1) 5 : 6
(2) 2 : 3
(3) 3 : 2
(4) 6 : 1

Answer 1

Answer:

5:6

Step-by-step explanation:

the roots are 5,6

so the ratio become=5:6

Answer 2

Answer:

$\large\boxed{\textnormal{\boxed{\textnormal{A. 5:6}, x=6, x=5}}}$

Step-by-step explanation:

To solve this problem, first you have to use quadratic equation formula.

Given:

x²-11x+30=0

Solutions:

First, you have to use quadratic equation formula.

$\large\boxed{\textnormal{Quadratic Equation Formula}}}$

$\displaystyle \frac{-b\pm \sqrt{b^2-4ac}}{2a}$

A=1

B=(-11)

C=30

$\displaystyle x_{1,\:2}=\frac{-\left(-11\right)\pm \sqrt{\left(-11\right)^2-4\cdot \:1\cdot \:30}}{2\cdot \:1}$

Solve.

$\displaystyle \frac{-\left(-11\right)+\sqrt{\left(-11\right)^2-4\cdot \:1\cdot \:30}}{2\cdot \:1}$

$\large\boxed{\textnormal{Apply Rule}}$

$\displaystyle -(-c)=c$

Rewrite the problem down.

$\displaystyle 11+\sqrt{(-11)^2-4*1*30}=12$

$\displaystyle \frac{12}{2*1}$

Multiply numbers from left to right.

$\displaystyle 2*1=2$

Divide.

$\displaystyle 12\div2=\boxed{6}$

$\displaystyle\frac{-\left(-11\right)-\sqrt{\left(-11\right)^2-4\cdot \:1\cdot \:30}}{2\cdot \:1}=\boxed{5}$

The solutions of quadratic equation is x=6, x=5.

Therefore, the correct answer is 5:6.